Hi there!
On my forum which I started a while back, we concluded that Windows 8 will improve your performance greatly.
Having upgraded from an i5 myself to an i7, I havn't noticed a great deal of performance gain in games (5% give or take a couple percent). The performance gain only came in video rendering software, such as After Effects or Premier Pro, which was quite significant in rendering times. Whatever you are considering, Windows 8 will be one of the biggest upgrades you can do in terms of performance.
So if you don't use CPU intensive programs (video editing, CAD- Computer Aided Design) then an i5 will be GREAT for gaming as most games use 2 cores on a CPU, Battlefield 4 is the only game to utilize not only 4 cores, but thanks to AMD's 5 million dollar investment into DICE, Battlefield 4 now takes advantage of an 8 Core CPU. If you decide for the i5, a decent cooler wouldn't go a miss, along with a decent overclocking motherboard, say a MSI GD-65 with a corsair H60i, then overclock to about 4.2Ghz or possibly 4.4 Ghz. Note the IvyBridge chips such as the i5 3570k and the i7 3770k WILL run hotter than the latest Haswell chips (i5 4570k and the i7 4770k)
If you want to stream on twitch, record or future proof your system, an upgrade to an 8 core (both hyper-threaded or 8 physical cores) isn't a bad idea. I noticed after upgrading to the i7, FRAPS and Dxtory recorded a lot better (mainly FRAPS, as Dxtory is more HDD dependant).
Conclusion in short: Solely gaming (No recording/editing) = i5 4670k or i5 3570k (around 2%-5% performance gain, but the Z77 motherboards are a bit cheaper than the Z87 by around £20-£60.
Recording/editing/furuteproofing = Any AMD FX 8000 chip or i7 will do (Intel perform better in single threaded applications, and don't choose the APUs!)
I hope this helped!